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DECIMALS, OR, DECIMAL FRACTIONS. A decimal fraction is a part of a unit, or whole number, numbering by ten.

As an apple, or a dollar, &c., being divided into ten equal parts, then one or more of those parts are called so many tenths: if into 100 equal parts, then any number of those parts are called so many hundredths. They are distinguished from whole numbers by a point or period set to their left

, thus, .5 denotes five-tenths 6 ), and .75 are called seventy-five hundredths 67). The notation and numeration of decimals are explained in the following table.

7 5 9 3 8

5 1 9 8 4 Ciphers annexed to decimals do not increase their value: thus, .1 or .10 are equal; but prefixed, decrease them in a tenfold proportion: thus, .1 or .01 are different–the last decimal is only one-tenth part as much.

ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS.

RULE.—Write down point under point, units under units, tens under tens, &c. : proceed to add or subtract as in whole numbers, and place the point in the sum total, or difference, directly under the points above, in the numbers given. Proof, the same as whole numbers.

EXAMPLES.

1. How many acres are in 4 fields containing as follows, viz46.75 acres, 25.5 acres, 36.25 acres, and 28.5 acres ? Ans. 137.

2. From one and six-tenths, take nine-tenths ? Ans. .7 tenths. 3. Add six-tenths, four-tenths, two-tenths, eight-tenths, and five.

Ans. 7. 4. From one, take one-thousandth.

Ans. .999. 5. Add $25., $5.75, $10.2, $9., and five cents. MULTIPLICATION AND DIVISION OF DECIMAL FRACTIONS. Rules the same as given in Multiplication and Division of Federal Money.

EXAMPLES. 1. What is the value.5 of a bushel of turnips, at $.125 per bushel ? 2. Multiply 2.68 by 25. Ans. 67.-3. Divide .8 by .8. Ans. 1. 4. How many .8 will make 8.

Ans. 10. Note.--When the divisor has more decimal places than the dividend, annex as many ciphers to the dividend, as will make the decimals in both equal. Annex, to place after. Prefix, to place before. 5. What will a man earn in 25.5 days, at $.75 per day?

Ans. $19.125 Questions. What is a decimal fraction ? Numbering by what? How designated from whole numbers ? Recite the rules of addition and subtraction. What is the rule of multiplication and division of decimals? What is the rule for pointing off decimals in the product?-quotient ?

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COMPOUND ADDITION.

COMPOUND ADDITION.

COMPOUND ADDITION is the adding of several quantities together, having different denominations, as dollars, cents, mills, or tons, hupdreds, quarters, &c.

RULE.

1. Place the numbers so that those of the same denomi. nation may stand directly under each other.

2. Add the right hand column or denomination together, as in whole numbers; then divide the sum by as many as the amount of the next higher denomination, setting down the remainder under the column added, and carry the

quotient to the next superior denomination, continuing the same to the last, which add as in Simple Addition.

PROOF-As in Addition.

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Note.--The above examples may be considered as more properly belonging to Simple Addition.

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1.

TROY WEIGHT.
1b. Ozdwt.
grs.

16.

0%. dwt. grs. 74 10 17 22 2. 32 11 18 13 39 6 14 16

68 9 10 21 5 11 16 19

41 10 13 7 342 0 2 5

4 6 15 12

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ft. in.

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COMPOUND ADDITION.

LONG MEASURE.
M. yd.

L. M. fur. P. yd. ft. in. 1. 85 1758 29 2. 25 2 7 36 - 4.5 2 11 36 1631 1 2

16 1 2 11 3 1 9 24 1072 0.5

47 2 4 24. 2.5 2 5 8 .621 2 10

12 0 1 8 6 0 10

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MOTION OR CIRCULAR MEASURE, sig.

sig. ° 1. 2 28 42 57

2. 3 19 39 51 1 17 57 38

2 27 54 32 1 -19 14 10

4. 28 14 12 2 24 26 43

14 11 25

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ft. in.

LAND OR SQUARE MEASURE.
A. R. P.

A. R. P. yd. 1. 265 3 36

2. 210 2 28 30 8 142 649 1 27

126 3 18 10 2 126 108 2 15

82 1 36 20.50 3 98 721 0 10

219 3 36 2 2 78

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SOLID OR CUBICAL MEASURE. Tons c.ft. s.in. yd. c.ft. c.in.

C. c.ft. c.in. 1. 26 38 1272 2. 75 26 1578 3. 64 125 1720 82 21 1695 12 20 1162

31 105 1017 14 19 452 74 16 1008

27 71 1210 8 14 1234 80 8 175

8 9 197

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LIQUID MEASURE.
T. pi. hhd. gal. qt. pt.

hhd. gal. qt. pt. 1. 15 1 1 61 3 1

2. 8 56 3 6 78 0 1 36 1 0

4 26 1 4 12 1 0 42 2 1

6 42 2 2 16 1 1 27 1 1

2 15 1 5

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bu. p. qt.

DRY MEASURE.
bu. p. qt. pt.
1. 64 3 6 1

2. 12 2 4
17 1 3 0

8 3 6 11 2 17 1

10 1 7 19 2 4 1

9 2 3

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COMPOUND SUBTRACTION. COMPOUND SUBTRACTION is the taking of a quantity of several denominations from a larger amount of like kind.

RULE.

Place the smaller quantity under the larger, so that the same denominations shall be under each other; then begin on the right hand, and subtract the lower quantity from the quantity above it, and set down the remainder: when the lower quantity is more than the upper, add to the upper quantity as many of that denomination, as make one of the next larger; then subtract, and set down the remainder carrying 1 to the next denomination, and so proceed the others.

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